The sum of 4.6 and one-third a number is equal to at most 39.1. What are all the possible values of the number? Artem wrote the inequality 1/3n+4.6≤39.1 , where n equals the number, to help solve this problem. Solve his inequality.

Question

n≤131.1
n≤11.5
n≤112.7
n≤103.5

Answer 1

To solve the inequality \( \frac{1}{3}n + 4.6 \leq 39.1 \):

1. Subtract 4.6 from both sides:

   \[ \frac{1}{3}n \leq 39.1 - 4.6 \]

   Calculate the right side:

   \[ 39.1 - 4.6 = 34.5 \]

   So, the inequality now reads:

   \[ \frac{1}{3}n \leq 34.5 \]

2. Multiply both sides by 3 to eliminate the fraction:

   \[ n \leq 34.5 \times 3 \]

   Calculate \( 34.5 \times 3 \):

   \[ 34.5 \times 3 = 103.5 \]

Therefore, the solution to the inequality is:

\[ n \leq 103.5 \]

From the options provided, the correct one is:

n ≤ 103.5

Answer 2

Twelve less than four-fifths of a number is more than 24. What are all the possible values of the number? Lucia wrote the inequality 45n−12>24 , where n equals the number, to help solve this problem. Solve her inequality.
n>9.6
n>15
n>28.8
n>45

Answer 3

To solve the inequality based on the problem statement, let's rewrite it step by step.

The problem states that "twelve less than four-fifths of a number is more than 24". We can express this mathematically as follows:

\[ \frac{4}{5}n - 12 > 24 \]

Now, let's solve the inequality.

1. Add 12 to both sides:

   \[ \frac{4}{5}n > 24 + 12 \]

   This gives:

   \[ \frac{4}{5}n > 36 \]

2. Multiply both sides by \( \frac{5}{4} \) to isolate \( n \):

   \[ n > 36 \times \frac{5}{4} \]

   Calculate \( 36 \times \frac{5}{4} \):

   \[ 36 \times \frac{5}{4} = 36 \times 1.25 = 45 \]

Thus, the solution to the inequality is:

\[ n > 45 \]

From the options provided, the correct one is:

n > 45

Answer 4

Ellie is saving to buy a phone. She wants to have at least $299 saved before buying one. She currently has $213 saved, and she receives $10 a week as an allowance from her parents. After how many weeks will Ellie have enough money saved? Ellie writes the inequality 10w+213≥299 , where w is the number of weeks, to help figure this out. Solve her inequality.
w≥86
w≥8.6
w≥51.2
w≥860

Answer 5

To solve the inequality that Ellie wrote, \( 10w + 213 \geq 299 \), where \( w \) is the number of weeks, we will follow these steps:

1. Subtract 213 from both sides:

   \[ 10w \geq 299 - 213 \]

   Calculate the right side:

   \[ 299 - 213 = 86 \]

   So, the inequality now reads:

   \[ 10w \geq 86 \]

2. Divide both sides by 10 to isolate \( w \):

   \[ w \geq \frac{86}{10} \]

   Calculate \( \frac{86}{10} \):

   \[ \frac{86}{10} = 8.6 \]

Thus, the solution to the inequality is:

\[ w \geq 8.6 \]

Since \( w \) represents the number of weeks, Ellie will need at least 9 weeks (since weeks must be whole numbers).

From the options provided, the correct one is:

w ≥ 8.6